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**stardust****Member**- Registered: 2006-04-09
- Posts: 48

I was doing my maths hw when i got stuck on this M1 exam paper question.

3. In a simple model for the motion of a car, its velocity,v, at time t seconds is given by

v=(3t² - 2t + 8)i + (5t +6)j ms-¹

a) Calculate the speed of the car when t=0.

b) Find the values of t for which the velocity of the car is parallel to the vector (i+j).

c) Why would this model not be appropriate for large values of t?

I have done a) and made it 10ms-¹ which agrees with the answers i have been supplied. I am confused on how to do b) and any help would be appreaciated.

Thanks

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,316

if a vector ai+bj is parallel to the vector i+j, it means ai+bj=k(i+j)

since i and j are not parallel to each other, the only solution is a=k, b=k

Hence a=b

for your question

3t² - 2t + 8=5t +6

3t²-7t+2=0

(3t-1)(t-2)=0

t=1/3 or t=2

for c, the speed cannot grow up forever.

**X'(y-Xβ)=0**

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**stardust****Member**- Registered: 2006-04-09
- Posts: 48

Thanks

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

Neat Answer.

Oh, and "c" is because of "c"

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,316

**X'(y-Xβ)=0**

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